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PubMed2003

Bioaerosol data distribution: probability and implications for sampling in evaluating problematic buildings.

Airborne fungal contamination in the indoor environment is a substantial contributor to indoor air quality (IAQ) problems, yet there are no set numerical standards by which to evaluate air sampling data. Intuitively appealing is the operational model that the indoor air should not be significantly different from the outdoor air, but determining what is "significant" as well as where to sample and how many samples to collect to determine significance have not been firmly established. The purpose of this study was to determine the number of samples and their locations necessary to determine significant differences in airborne fungi between the ambient and indoor environments. Sampling results from several hundred air samples for culturable fungi from various sites were used to derive a probability of detection in the outdoor air for problematic or "marker" fungal species. Under the assumption that indoor fungal growth results in an increase in the probability of detection for a given fungal species, mathematical probability dictates the number of samples necessary in the indoor (target zone) and in the outdoor (reference zone) air to demonstrate significance. Ultimately, it is the sparse distribution of the problematic species that drives the number of required samples to demonstrate a significant difference, which varies depending upon the level of significance desired. Therefore, the number of samples in each zone can be adjusted to reach a target difference in detection frequency, or an investigator can assess a sampling scheme to identify the differences in detection frequency that show significance.

Aerosols↗

PubMed2000

A probability model for evaluating building contamination from an environmental event.

Asbestos dust and bioaerosol sampling data from suspected contaminated zones in buildings allowed development of an environmental data evaluation protocol based on the differences in frequency of detection of a target contaminant between zones of comparison. Under the assumption that the two test zones of comparison are similar, application of population proportion probability calculates the significance of observed differences in contaminant levels. This was used to determine whether levels of asbestos dust contamination detected after a fire were likely the result of smoke-borne contamination, or were caused by pre-existing/background conditions. Bioaerosol sampling from several sites was also used to develop the population proportion probability protocol. In this case, significant differences in indoor air contamination relative to the ambient conditions were identified that were consistent with the visual observations of contamination. Implicit in this type of probability analysis is a definition of "contamination" based on significant differences in contaminant levels relative to a control zone. Detection of a suspect contaminant can be assessed as to possible sources(s) as well as the contribution made by pre-existing (i.e., background) conditions, provided the test and control zones are subjected to the same sampling and analytical methods.

Aerosols↗

PubMedDate not supplied

Improving doctor-patient understanding of probability in communicating cancer-screening test findings.

Several researchers have questioned the merits of early mammography and prostate-specific-antigen (PSA) screening policies, arguing that these programs have not been proven useful in lowering mortality rates. This controversy highlights the necessity and importance of effectively communicating probability information to patients. Probability information, however, has been plaguing the health care profession--as numerous investigators have shown that it is often difficulty to understand and transmit. These difficulties can be overcome by changing the presentation format from a probabilistic format to a frequency format, thereby enhancing doctors' and patients' ability to solve and understand statistical information. Although I highlight this problematic issue with a discussion of mammography and prostate-specific-antigen screening, the suggested solution is not confined to a single medical procedure, but can be extended to any other medical domains where doctors are faced with the difficult task of providing complex probability data to patients.

Breast Neoplasms↗

PubMed2003

A quantitative assessment of factors influencing the probability of postmarketing out-of-specification observations.

When marketed lots of pharmaceutical products produce a number of out-of-specification (OOS) samples, it can be very disruptive. In some cases such lots must be recalled, at substantial expense. We present a model of the probability of OOS samples and show quantitatively how this probability depends on the underlying variation and on the original stability study. We describe the limited situations in which sponsors can reduce the probability of OOS samples.

Drug Stability↗

PubMed2003

Estimating and comparing correct-use failure probabilities in clinical studies of condom functionality.

In a clinical study comparing the failure probabilities of two condom types, the sample of all reported acts of intercourse in which a study condom was used by a randomized participant is typically defined to be the primary analysis sample. However, it may also be desirable to make comparisons among only those acts in which the participants correctly followed all condom use instructions before, during, and after the act of intercourse (i.e., the "correct-use" subset). The timing associated with the definition of correct use creates a dilemma in that an act cannot be classified as a "correct-use act" until after the completion of both intercourse and withdrawal; if a condom fails (e.g., breaks or slips completely off of the penis) during intercourse then the couple has no chance at correct use during withdrawal. As a result of the implicitly conditional nature of this problem, it is not a simple matter to specify a correct-use subset of the primary analysis sample. With this in mind, we develop estimators for the correct-use failure probabilities, the corresponding standard errors, and test statistics for comparing the correct-use failure probabilities between condom groups. We demonstrate the utility of the proposed methods by applying them to data from a clinical study of condom contraceptive effectiveness, and we use simulated data to investigate the finite sample properties of the proposed methods. The simulation results indicate that one of our proposed estimators is at least approximately unbiased, even in small samples. Furthermore, one-sided noninferiority tests performed using this estimator tend to have sizes that are only marginally larger than the nominal test size in moderate to large samples.

Computer Simulation↗

PubMed2005

Type I error probabilities based on design-stage strategies with applications to noninferiority trials.

When testing the equality of means from two different populations, a t-test or large sample normal test tend to be performed. For these tests, when the sample size or design for the second sample is dependent on the results of the first sample, the type I error probability is altered for each specific possibility in the null hypothesis. We will examine the impact on the type I error probabilities for two confidence interval procedures and procedures using test statistics when the design for the second sample or experiment is dependent on the results from the first sample or experiment (or series of experiments). Ways for controlling a desired maximum type I error probability or a desired type I error rate will be discussed. Results are applied to the setting of noninferiority comparisons in active controlled trials where the use of a placebo is unethical.

Controlled Clinical Trials as Topic↗

PubMed1981

Hit probability for cellular targets by bone-surface-seeking alpha emitters.

Irradiation of cellular targets near bone surfaces with surface-seeking alpha-emitters is discussed in terms of hit probabilities to spheres. The geometrical factor describing the average number of hits as a function of distance from the surface is shown to be approximately proportional to the dose rate over most of the particle range. The hit probability is calculated for the case of a non-uniform distribution of cell nuclei at the bone surfaces of the thoracic vertebrae of beagles. The effect of a spatial variation of the specific surface activity and burial depth along bone surfaces is evaluated and a general expression derived, relating the hit probability to the dose rate distribution. From this expression numerical results are calculated using measured dose rate distributions in the lumbar vertebrae of rats. The validity of the underlying assumption and the consequences with respect to tumour models are discussed.

Alpha Particles↗

PubMed1994

Probability of autocrine ligand capture by cell-surface receptors: implications for ligand secretion measurements.

Autocrine ligands regulate important cell behavioral functions in both physiological and pathological conditions. Binding of these ligands to cell-surface receptors involves more subtle considerations than that of exogenous (endocrine or paracrine) ligands. Autocrine secretion leads to a release of molecules in the local microenvironment proximal to the cell surface, thus allowing interaction with receptors to compete directly with diffusive loss to the bulk extracellular medium. Complications in autocrine systems due to this binding vs. transport competition arise in at least three aspects: (i) experimental measurement of autocrine ligand secretion rates is compromised; (ii) kinetics of autocrine ligand binding to cell-surface receptors are difficult to follow; and (iii) inhibition by exogenous blockers of autocrine ligand binding to cell receptors is problematic. At the heart of all these complications is the need to determine the fractional distribution of the secreted autocrine ligand between cell-surface receptor capture and diffusive loss to the bulk media. In this paper we offer a theoretical treatment of this problem using Brownian dynamics simulation techniques to calculate the capture probability of the cell receptors for the autocrine ligand. A major result is that the capture probability is significantly lower than the predicted by the Berg-Purcell steady-state diffusion approach. Another is that the capture probability is essentially independent of release location. Implications of these results for the complications found in autocrine systems are discussed.

Algorithms↗

PubMed1995

Pathology and probability. Likelihood ratios and receiver operating characteristic curves in the interpretation of bronchial brush specimens.

Diagnoses in pathology often are qualitative, such as atypical or suspicious, and consequently are thought to have limited clinical value. To investigate the utility of a qualitative diagnostic system, seven pathologists retrospectively evaluated 100 bronchial brush specimens using the following categories: definitely benign, probably benign, possibly malignant, probably malignant, and definitely malignant. The likelihood ratio (LR) and receiver operating characteristic (ROC) curve, two statistical probabilistic measurements, were used to calculate diagnostic accuracy among individuals and groups. The results show: (1) the LR for individual diagnostic categories varied among observers, resulting in different clinically malignant probabilities; (2) observer experience did not appear to play a role in overall diagnostic accuracy, except in the diagnosis of small cell carcinoma; (3) observers operate at higher levels of diagnostic accuracy with, rather than without, clinical history. The authors conclude that qualitative diagnoses contain important information and can be interpreted effectively with LR and ROC.

Bronchi↗

PubMed1989

Methods for calculating the probabilities of finding patterns in sequences.

This paper describes the use of probability-generating functions for calculating the probabilities of finding motifs in nucleic acid and protein sequences. Equations and algorithms are given for calculating the probabilities associated with nine different ways of defining motifs. Comparisons are made with searches of random sequences. A higher level structure--the pattern--is defined as a list of motifs. A pattern also specifies the permitted ranges of spacing allowed between its constituent motifs. Equations for calculating the expected numbers of matches to patterns are given.

Algorithms↗

PubMed2026

LinearCapR: linear-time computation of per-nucleotide structural-context probabilities of RNA without base-pair span limits.

MOTIVATION: RNA molecules adopt dynamic ensembles of secondary structures, where the local structural context of each nucleotide-such as whether it resides in a stem or a specific type of loop-strongly shapes molecular interactions and regulatory function. Structural-context probabilities therefore provide a more functionally informative view of RNA folding than the minimum free energy structures or base-pairing probabilities. However, existing tools either require O(N3) time or employ span-restricted approximations that omit long-range base-pairs, limiting their applicability to large and biologically important RNAs. RESULTS: We introduce LinearCapR, enabling linear-time, span-unrestricted computation of structural-context marginalized probabilities, using beam-pruned Stochastic Context Free Grammar-based computation. LinearCapR retains global ensemble features lost by span-limited methods and yields superior predictive power on bpRNA-1m(90) dataset, especially for multiloops and exterior regions, as well as long-distance stems. LinearCapR supports analysis of long RNAs, demonstrated on the full genome of SARS-CoV-2. LinearCapR provides the first base-pair-span-unrestricted, linear-time framework for RNA structural-context analysis, retaining key thermodynamic ensemble features essential for functional interpretation. It enables large-scale studies of viral genomes, long non-coding RNAs, and downstream analyses such as RNA-binding protein site prediction. AVAILABILITY AND IMPLEMENTATION: The source code of LinearCapR is available at https://github.com/hoget157/LinearCapR. The archived software release used in this work is available at Zenodo: https://doi.org/10.5281/zenodo.19450645.

Nucleic Acid Conformation↗

PubMed1985

Induction of papillomas with a high probability of conversion to malignancy.

Papillomas induced by standard initiation-promotion protocols progress to carcinomas at a low frequency. Experimental protocols were developed to elicit papillomas with a higher probability of malignant conversion. SENCAR mice initiated by 7,12-dimethylbenz[a]anthracene were promoted by treatment with 12-O-tetradecanoylphorbol-13-acetate (TPA) for 5, 10, 20 or 40 weeks. With promotion for 10 weeks or more, a peak of papilloma incidence at 16-20 weeks was followed by a 35-40% decrease within 3 months. A much lower papilloma response was seen in mice promoted for 5 weeks, but these papillomas persisted. The yield of malignant tumors was similar in all four groups, with 20-25 carcinomas per group of 30 mice. Thus, the papillomas induced by the first few TPA treatments are much more likely to progress to carcinomas than those which appear later. In a separate study, initiated Charles River CD-1 mice were promoted with TPA for either 12 or 52 weeks. Acetone solvent treatment was begun at Week 13 in the group treated 12 weeks with TPA. At Week 16, the papilloma incidence was identical in the two groups of mice. However, by Week 28, the papilloma yield in the continuous TPA group had increased and was twice that of the acetone group, in which papillomas had regressed. The first carcinoma arose 14 weeks earlier with continuous TPA, but the final number of carcinomas per group of 40 mice was 17 with TPA and 20 with acetone. Neither the increase in papillomas in TPA-treated mice nor the regression of papillomas after cessation of promotion with TPA affected the final carcinoma yield. This result suggests that TPA-dependent papillomas are very unlikely to progress to carcinomas. In a third experiment, promotion of initiated SENCAR mice with mezerein resulted in a small number of papillomas which had a much higher probability of progression to carcinomas than the large number of papillomas promoted by TPA. The ability to induce papillomas promoted by TPA. The ability to induce papillomas with a known probability of conversion to carcinomas will facilitate the identification of markers associated with malignant progression.

9,10-Dimethyl-1,2-benzanthracene↗

PubMed1997

An index of information content for genotype probabilities derived from segregation analysis.

A genotype probability index (GPI) is proposed to indicate the information content of genotype probabilities derived from a segregation analysis. Typically, some individuals are genotyped at a marker locus or a quantitative trait locus, and segregation analysis is used to make genotype inferences about ungenotyped relatives. Genotype probabilities for a two-allele autosomal locus are plotted on a triangular surface. The GPI has a value of zero at the point corresponding to Hardy-Weinberg frequencies, and a value of 100% at the vertices of the triangle. Trigonometric functions are used to help calculate intermediate index values. It is proposed that such an index can be useful to help identify which ungenotyped individuals or loci should be genotyped to maximize the benefit/cost of genotyping operations.

Genotype↗

PubMed1997

The probability of fixation in populations of changing size.

The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

Alleles↗

PubMed2000

The probability of duplicate gene preservation by subfunctionalization.

It has often been argued that gene-duplication events are most commonly followed by a mutational event that silences one member of the pair, while on rare occasions both members of the pair are preserved as one acquires a mutation with a beneficial function and the other retains the original function. However, empirical evidence from genome duplication events suggests that gene duplicates are preserved in genomes far more commonly and for periods far in excess of the expectations under this model, and whereas some gene duplicates clearly evolve new functions, there is little evidence that this is the most common mechanism of duplicate-gene preservation. An alternative hypothesis is that gene duplicates are frequently preserved by subfunctionalization, whereby both members of a pair experience degenerative mutations that reduce their joint levels and patterns of activity to that of the single ancestral gene. We consider the ways in which the probability of duplicate-gene preservation by such complementary mutations is modified by aspects of gene structure, degree of linkage, mutation rates and effects, and population size. Even if most mutations cause complete loss-of-subfunction, the probability of duplicate-gene preservation can be appreciable if the long-term effective population size is on the order of 10(5) or smaller, especially if there are more than two independently mutable subfunctions per locus. Even a moderate incidence of partial loss-of-function mutations greatly elevates the probability of preservation. The model proposed herein leads to quantitative predictions that are consistent with observations on the frequency of long-term duplicate gene preservation and with observations that indicate that a common fate of the members of duplicate-gene pairs is the partitioning of tissue-specific patterns of expression of the ancestral gene.

Biological Evolution↗

PubMed1976

Remarriage probability after widowhood: a retrospective method.

A technique was devised to estimate age specific remarriage probabilities for newly widowed persons utilizing North Carolina marriage certificates plus informatiom from the 1970 U. S. Census. Remarriage probabilities are very high for persons widowed before age 35. Remarriage probabilities decrease faster for widows than widowers. Less than one-fourth of men widowed after age 65 ever remarry. Less than 5% of women widowed after age 55 ever remarry. Age specific intervals to remarriage were also calculated. Men remarry more quickly than women. The median interval to remarriage was 1.7 years for men and 3.5 years for women.

Black or African American↗

PubMed2006

Among patients treated for IVF with gonadotrophins and GnRH analogues, is the probability of live birth dependent on the type of analogue used? A systematic review and meta-analysis.

This systematic review and meta-analysis aimed to answer the following clinical question: among patients treated for IVF with gonadotrophins and GnRH analogues, is the probability of live birth per randomized patient dependent on the type of analogue used? Eligible studies were randomized controlled trials (RCTs), published as a full manuscript in a peer-reviewed journal, that contained sufficient information to allow ascertainment of whether randomization was true and whether equality was present between the groups compared. A literature search identified 22 RCTs comparing GnRH antagonists and GnRH agonists that involved 3176 subjects. Where live birth was not reported in a study that fulfilled the inclusion criteria, an effort was made to contact the corresponding authors to retrieve the missing information. If this was not possible, the reported outcome measure, clinical pregnancy or ongoing pregnancy was converted to live birth in 12 studies using published data (Arce et al., 2005). No significant difference was present in the probability of live birth between the two GnRH analogues [odds ratio (OR), 0.86; 95% confidence intervals (CI), 0.72 to 1.02]. This result remains stable in subgroup analysis that ordered the studies by type of population studied, gonadotrophin type used for stimulation, type of agonist protocol used, type of agonist used, type of antagonist protocol used, type of antagonist used, presence of allocation concealment, presence of co-intervention and the way the information on live birth was retrieved. In conclusion, the probability of live birth after ovarian stimulation for IVF does not depend on the type of analogue used for pituitary suppression.

Female↗

PubMed1994

Assignment of position-specific error probability to primary DNA sequence data.

DNA sequence predicted from polyacrylamide gel-based technologies is inaccurate because of variations in the quality of the primary data due to limitations of the technology, and to sequence-specific variations due to nucleotide interactions within the DNA molecule and with the gel. The ability to recognize the probability of error in the primary data will be useful in reconstructing the target sequence of a DNA sequencing project, and in estimating the accuracy of the final sequence. This paper describes the use of linear discriminant analysis to assign position-specific probabilities of incorrect, over- and under-prediction of nucleotides for each predicted nucleotide position in primary sequence data generated by a gel-based DNA sequencing technology. Using this method, most of the error potential in primary sequence data can be assigned to a limited number of discrete positions. The use of probability values in the sequence reconstruction process, and in estimating the accuracy of consensus sequence determination is described.

Base Sequence↗